Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.

Inverse Problems in Solid Mechanics and Ultrasonic

The IP （inverse problem） in solid mechanics have emerged through the 20th century and measured. Nowadays has accept the classification of inverse problems in solid mechanics [1]： retrospective IP, boundary IP, coefficient IP, geometric IP. The IPs in theory of elasticity, theory of plasticity, theory of strengthening, fatigue theory, fracture theory micro-structural of polycrystalline materials are formulated and solved. The method of high frequency theory of ultrasonic waves is used. The results which are obtained here show, that all coefficients and geometrical characteristics of imperfections in the material are functions only of longitudinal and transversal velocities and attenuation of ultrasonic waves, which are measured, according ASTM E 494： 2015. The received relationships from this article could be used for NDE （non-destructive evaluation） of the coefficients and the geometrical characteristics of imperfections in polycrystalline materials.

THE PROBLEM OF INEQUALITY IN SOLID MECHANICS

In this paper the problem of inequality in solid mechanics, the contents of which consist of some main concepts, methods and results of the stationary and evolutionary as well as determinate and random problems in variational principle and variational ine -quality, is studied in detail.

Mossbauer Spectroscopic Studies on a Supersaturated Solid Solution of Fe-Cu Formed by Mechanical Alloying

Mechanical alloying (MA) was employed to produce supersaturated solid solutions of Fe1-xCux,which is virtually immiscible under an equilibrium condition at ambjent temperature. The X-ray diffraction results show that the solutions formed in the concentration ranges of x≤0.1 5 and x≥0.40 are of bcc structure of iron and fcc structure of copper. respectively. For the region in between.however, the alloy obtained is a mixture of bcc plus fcc phases. The Mossbauer spectrum of the solid solution of a single phase could be fitted by two sub-spectra with hyperfine magnetic fields of 200 and 250 kOe. respectively. suggesting that there must exist two forms of coordination in the solution. While to fit the spectrum for the solution with mixed structu re. three Sub-spectra. including a spectrum of α-Fe, should be used. The variation of the Mossbauer spectra of Fe60Cu40 with milling time as well as annealing temperature was systematically studied. This may be ascribed to the changes of the number of nearest neighboring atoms of iron in the processes of formation and decomposition of the solid solution during milling and annealing

Solid reaction mechanism of CaHPO_4·2H_2O + CaCO_3 with and without yttria

The effect of yttria on the solid reaction mechanism of a CaHPO4·2H2O ＋ CaCO3 system at different temperatures was experimentally stud-ied. The samples with and without yttria were subjected to thermogravimetric/differential scanning calorimetry measurement. The samples were heat treated at the temperatures corresponding to the peaks on the DSC spectra, and the resulted phase compositions were identified by X-ray diffraction. The transformation mechanism was deduced by comparing the phases obtained at different temperatures. The results show that the transformations at below 1073 K are not affected by yttria, but all those at above 1073 K are completely altered. The formation tem-perature of hydroxyapatite decreases by 134 K, and the decomposition temperature increases by 38 K. The polymorphous transformation of Ca3（PO4）2 from β phase to α phase increases by 47 K. The thermodynamic properties of the transformations at above 1073 K are also modi-fied by the addition of yttria; that is, the endothermal peaks are substituted by exothermal peaks.

Role of Microstructure and Spectrum Features on the Catalysis Effect of Ce1-x(Nd0.5Eu0.5)xO2-δSolid Solutions

Nanosized Ce^1-x）（Nd^0.5）Eu^0.5））xO^2-δ） solid solutions（x = 0.00-0.20） were synthesized by means of hydrothermal method.Then the solid solutions were ball milled with Mg2Ni and Ni powders for 20 h to get the Mg2Ni–Ni–5 mol% Ce^1-x）（Nd^0.5）Eu^0.5））xO^2-δ） composites.The structures and spectrum characteristics of the Ce^1-x）（Nd^0.5）Eu^0.5））xO^2-δ） solid solutions catalysts were analyzed systemically.XRD results showed that the doped samples exhibited single phase of CeO2 fluorite structure.The cell parameters and cell volumes were increased with increasing the doped content.Raman spectrum revealed that the peak position of F^2g mode shift to higher wavenumbers and the peak corresponding to oxygen vacancies were observed distinctly for the doped samples.UV-Vis technique indicated that the absorption peaks of Eu^3＋ and Nd^3＋ ions appeared; the bandgap energy was decreased linearly.The electrochemical and kinetic properties of the Mg2Ni–Ni–5 mol% Ce1-x（Nd0.5Eu0.5xO2-δ composites were measured.The maximum discharge capacity was increased from 722.3 mA h/g for x = 0.00 to 819.7 mA h/g for x = 0.16,and the cycle stability S20 increased from 25.0%（x = 0.00） to 42.2%（x = 0.20）.The kinetic measurement proved that the catalytic activity of composite surfaces and the hydrogen diffusion rate were improved for the composites with doped catalysts,especially for the composites with x = 0.16 and x = 0.20.The catalysis mechanism was analyzed from the point of microstructure and spectrum features of the Ce1-x（Nd0.5Eu0.5）xO2-δ solid solutions.

Penetration depth for yaw-inducing bursting layer impacted by projectile

In order to accurately estimate the anti-penetration capacity of yaw-inducing bursting layer with irregular barriers on surface impacted by projectile,the theoretical model of attack angle and angular velocity for projectile impacting on irregular barrier was achieved according to the macroscopic relation of contact force versus contact time,in which the main factors such as the relative geometrical characteristics of projectile and irregular barrier,material property and impact velocity of projectile influencing on yaw-inducing effectiveness were considered.On the basis of considering synthetically the influences of attack angle,impact velocity,impact angle of projectile and uncontrolled free surface of target,the theoretical formulation of penetration depth for bursting layer with irregular barriers on surface impacted by projectile was presented by expressing the stress of an optional point on the nose of projectile according to the relation of stress versus velocity.The theoretical results indicate that in the case of oblique impact embodying effect of attack angle,the penetration depth is reduced with the increase of impact angle,attack angle or angular velocity,and penetration trajectory is also deflected obviously.The effectiveness of angular velocity influencing on penetration depth is increased with impact velocity increasing.The theoretical results are in good agreement with test data for low impact velocity.

A STUDY ON THE COUNTER-INTUITIVE BEHAVIORS OF PIN-ENDED BEAMS UNDER PROJECTILE IMPACT

The counter-intuitive behaviors of pin-ended beams under the projectile impact axe investigated with ANSYS/LS-DYNA in this paper. It studies in detail their displacement-time history curves, final deformed shapes, energy relationships and projectile impact velocity ranges related to their counter-intuitive behaviors. The influences of the impact positions on their counterintuitive behaviors are also discussed. The results show that no matter where the impact position on the beam is, the counter-intuitive behaviors of pinned beams will occur as long as the impacting velocity lies within a proper range. Corresponding to the occurring of the counter-intuitive behaviors, the rebounding number in the displacement history curves of the beams decreases from a few times to zero with an increase of the impact velocity. The final deformation modes of the beam corresponding to the counter-intuitive behaviors will appear in symmetrical and unsymmetrical forms no matter where the impact position is; the impact velocity of the first-occurring of the counter-intuitive behaviors of the beam increases slowly with the deviation of the impact position away from the mid-span.

Finite Element Analysis of Smart Structures with Piezoelectric Sensors/Actuators Including Debonding

In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes to the static and dynamic response. In thepresent paper, an novel Enhanced Assumed Strain(EAS) piezoelectric solid element formulation isdeveloped for vibration active control of laminated structures bonded with piezoelectric sensors andactuators. Unlike the conventional brick elements, the present formulation is very reliable, moreaccurate, and computationally efficient and can be used to model the response of shell structuresbesides thin plates. Delaminations are modeled by pairs of nodes with the same coordinates butdifferent node numbers, and numerical results demonstrate the performance of the element and theglobal and local effects of debonding sensors/actuators on the dynamics of the adaptive laminates.

Pressure State in Deep Crust and Formation Depth of UHP Metamorphic Rocks

This paper presents some questions to the formula of pressure=depth×specific gravity from the viewpoint that the hydrostatic pressure is equal to the gravity of overlying rocks and the rocks in a static fluid state, which is drawn from the research and analysis of the research field and the corresponding problems of the pressure state in the deep crust and the formation depth of the UHP metamorphic rocks. In this research, the underground rocks are considered as the solid possessing some rheological behaviors to discuss the polysource stress state and to obtain a more reasonable method for the calculation of depths using the model of the unbalanced force solid. It is suggested from this paper that the P/SW method for the calculation of the ultrahigh pressure stemming only from the gravity has obviously overstated the formation depth of the UHP metamorphism. The formation model emphasizing the effect of the gravity, the tectonic force and the metamorphic force of the facies change concludes that such UHP minerals as coesite may have been produced in the inner crust.

Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks.

Mining pressure monitoring and analysis in fully mechanized backfilling coal mining face-A case study in Zhai Zhen Coal Mine

Fully mechanized solid backfill mining(FMSBM) technology adopts dense backfill body to support the roof. Based on the distinguishing characteristics and mine pressure control principle in this technology, the basic principles and methods for mining pressure monitoring were analyzed and established. And the characteristics of overburden strata movement were analyzed by monitoring the support resistance of hydraulic support, the dynamic subsidence of immediate roof, the stress of backfill body, the front abutment pressure, and the mass ratio of cut coal to backfilled materials. On-site strata behavior measurements of 7403 W solid backfilling working face in Zhai Zhen Coal Mine show that the backfill body can effectively support the overburden load, obviously control the overburden strata movement, and weaken the strata behaviors distinctly. Specific performances are as follows. The support resistance decreases obviously; the dynamic subsidence of immediate roof keeps consistent to the variation of backfill body stress, and tends to be stable after the face retreating to 120-150 m away from the cut. The peak value of front abutment pressure arises at 5-12 m before the operating face, and mass ratio is greater than the designed value of 1.15, which effectively ensures the control of strata movement. The research results are bases for intensively studying basic theories of solid backfill mining strata behaviors and its control, and provide theoretical guidance for engineering design in FMSBM.

Multiscale modeling of heterogeneous propellants from particle packing tograin failure using a surface-based cohesive approach

In the present work, a computational frame- work is established for multiscale modeling and analysis of solid propellants. A packing algorithm, considering the am- monium perchlorate （AP） and aluminum （A1） particles as spheres or discs is developed to match the size distribution and volume fraction of solid propellants. A homogenization theory is employed to compute the mean stress and strain of a representative volume element （RVE）. Using the mean results, a suitable size of RVE is decided. Without consider- ing the interfaces between particles and matrix, several nu- merical simulations of the relaxation of propellants are per- formed. The relaxation effect and the nonlinear mechanical behavior of propellants which are dependent on the applied loads are discussed. A new technology named surface-based cohesive behavior is proposed to describe the phenomenon of particle dewetting consisting of two ingredients： a damage initiation criterion and a damage evolution law. Several ex- amples considering contact damage behavior are computed and also nonlinear behavior caused by damaged interfaces is discussed in this paper. Furthermore the effects of the criti- cal contact stress, initial contact stiffness and contact failure distance on the damaged interface model have been studied.

Mechanical behaviors of NiAl-Cr(Mo)-based near eutectic alloy with Ti, Hf, Nb and W additions

Effects of Ti, Hf, Nb and W alloying elements addition on the microstructure and the mechanical behaviors of NiAl-Cr（Mo） intermetallic alloy were investigated by means of XRD, SEM, EDX and compression tests. The results show that Ni-31Al-30Cr-4Mo-2（Ti, Hf, Nb, W） alloy consists of four phases： NiAl, ？？Cr solid solution, Cr2Nb and Ni2Al（Ti, Hf）. The mechanical properties are improved significantly compared with the base alloy. The compression yield strength at 1 373 K is 467 MPa and the room temperature compression ductility is 17.87% under the strain rate of 5.56？？0-3 s-1, due to the existence of Cr2Nb and Ni2Al（Ti, Hf） phases for strengthening and Ti solid solution in NiAl matrix and coarse Cr（Mo, W） solid solution phase at cellular boundaries for ductility. The elevated temperature compression deformation behavior of the alloy can be properly described by power-law equation： ε=0.898 σ8.47exp[-615/（RT）].

On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations

This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.

Solid catalytic growth mechanism of micro-coiled carbon fibers

Micro-coiled carbon fibers were prepared by catalytic pyrolysisof acetylene with nano-sized nickel powder catalyst using the substrate method. The morphology of micro-coiled carbon fibers was observed through field emission scanning electron microscopy. It was found that the fiber and coil diameter of the obtained micro-coiled carbon fibers is about 500—600 nm and 4—5 μm, respectively. Most of the micro-coiled carbon fibers obtained were regular double carbon coils, but a few irregular ones were also observed. On the basis of the experimental observation, a solid catalytic growth mechanism of micro-coiled carbon fibers was proposed.

Origin of strong solid solution strengthening in the CrCoNi-W medium entropy alloy

Solid solution strengthening is one of the most conventional strategies for optimizing alloys strength,while the corresponding mechanisms can be more complicated than we traditionally thought specifically as heterogeneity of microstructure is involved.In this work,by comparing the change of chemical distribution,dislocation behaviors and mechanical properties after doping equivalent amount of tungsten(W)atoms in CrCoNi alloy and pure Ni,respectively,it is found that the alloying element W in CrCoNi alloy resulted in much stronger strengthening effect due to the significant increase of heterogeneity in chemical distribution after doping trace amount of W.The large atomic scale concentration fluctuation of all elements in CrCoNi-3W causes dislocation motion via strong nanoscale segment detrapping and severe dislocation pile up which is not the case in Ni-3W.The results revealed the high sensitivity of elements distribution in multi-principle element alloys to composition and the significant consequent influence in tuning the mechanical properties,giving insight for complex alloy design.

光滑粒子流体力学方法在流体、固体和生物力学中的应用

光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)作为最早发展的无网格粒子方法之一,对于模拟爆炸、冲击等涉及大变形问题,具有广阔的发展前景.本文对SPH方法在流体、固体和生物力学领域的改进算法和工程应用进行了全面介绍.阐述了SPH的基本理论和高精度SPH改进算法,分析了流体、固体和生物力学领域的改进技术.在模拟流体问题时,采用δ-SPH和GSPH方法解决了流体不稳定性的问题,并且讨论了流固耦合中的界面接触方法.针对固体的数值模拟,总结了三种传统改进方法(如应力点法、守恒光滑法、人工应力法)和Total Lagrangian SPH方法,改善了拉伸不稳定性问题;在生物力学方面,阐述了SPH控制方程和相互作用力的计算方法.本文综述了近年来SPH方法的应用进展,包括复杂海洋工程中的流固耦合问题,固体领域的天体、岩土力学、爆炸冲击以及增材制造等工程应用和生物力学中血流动力学、肠道健康和植物生长等典型应用;并分析了国内外SPH软件的发展,介绍了多尺度自适应分辨率方法、并行计算方法和网格自动生成技术来克服数值模拟方法在计算效率和计算规模上的限制.最后对目前存在的问题进行总结与展望,包括提高SPH算法的数值精度、如何精确描述固体的损伤与断裂问题和计算精度与效率之间的平衡等.在未来研究中,建立多尺度耦合SPH模型和深度学习将是进一步拓宽SPH方法应用的重要方向.

Static analysis of elastic cable structures under mechanical load using discrete catenary theory

In this paper,the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory.A cable net is discretized into multiple nodes and edges in our numerical approach,which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation.A fully implicit framework is proposed based on the discrete differential geometry(DDG)theory.The equilibrium configuration of a target object is derived by adding damping force into the system,known as the dynamic relaxation method.The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation.A more intricate scenario is further discussed in detail,where a structure consisting of multiple slender cables is connected through joints.Utilizing the robustness and efficiency of our discrete numerical framework,a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers.Finally,an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties,material characteristics,component numbers,and cable orientations.Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures,and could motivate innovative designs in both mechanical and civil engineered equipment.